Question

exponents
product rule & power rule

base | exponent / power
--- | --- | --- | --- | --- | --- | --- | ---
1 | | 1 | | | | |
2 | | | | | | |
3 | | | | | | |
4 | | | | | | |

evaluate the following exponential expressions. use the table.

1. $2^2 \cdot 2^3$
2. $3^1 \cdot 3^3$
3. $4^2 \cdot 4^3$
4. $2^1 \cdot 2^2$
5. $3^2 \cdot 3^3$
6. $4^5 \cdot 4^0$

what is the rule for multiplying with the same base?

can you write $3^2 \cdot 2^3$ as a single base and exponent? why or why not?

base | exponent / power
--- | --- | --- | --- | --- | --- | --- | ---
10 | | | | | | |

what is special about 10 raised to a power?
evaluate the following exponential expressions. use the table.

1. $10^2 \cdot 10^3$
2. $10^1 \cdot 10^6$
3. $10^5 \cdot 10^3$

Explanation:

Step1: Recall the Product Rule for Exponents

The product rule for exponents states that when multiplying two exponential expressions with the same base, we add the exponents. The formula is \( a^m \cdot a^n = a^{m + n} \), where \( a \) is the base and \( m, n \) are the exponents.

Step2: Apply the Rule to \( 2^2 \cdot 2^3 \)

For the expression \( 2^2 \cdot 2^3 \), the base \( a = 2 \), \( m = 2 \), and \( n = 3 \). Using the product rule, we add the exponents: \( 2^{2 + 3} = 2^5 \).

Step3: Calculate \( 2^5 \)

We know that \( 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32 \).

Answer:

\( 32 \)